Abstract [en]

We construct a calculus for generalized SG Fourier integral operators, extending known results to a broader class of symbols of SG type. In particular, we do not require that the phase func- tions are homogeneous. An essential ingredient in the proofs is a general criterion for asymptotic expansions within the Weyl-Hörmander calculus. We also prove the L^2(R^d)-boundedness of the generalized SG Fourier integral operators having regular phase functions and amplitudes uni- formly bounded on R^{2d}.